The appropriate choices appear to be the ones indicated.
A. The function g(x) is shifted right 2 places and up 3 places from f(x). It could be written
... g(x) = f(x -2) +3
We assume this is the intent of the arrow notation used: f(x) → g(x).
B. The function goes through (1, 0) and (5, 1), consistent with a log that has a base of 5.
The answers seem to be as shown in the attachment.